Which transitions result in the emission of visible light
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Consequently, the Bohr model retains a place in chemistry courses, even though it cannot be applied to other atoms. In setting up his model, Bohr designated zero energy as the point where the proton and electron are completely separated, level infinity. This energy level represents the highest potential energy state. Moving the electron to any of its lower allowed energy states within the atom results in a decrease in potential energy; a release of energy; and an energy level below zero, i.
Hence the minus sign in the above equation. When an excited-state electron drops back to a lower-energy state, it releases potential energy in the form of light. Some of the possible transitions are shown below. This is shown in the equations below:. The energy difference between levels gets smaller as levels increase. In the gas discharge tube, a high-energy beam of electrons strike the ground state hydrogen atoms, promoting the electron in each atom to higher-energy levels.
The electron may be promoted to different higher-energy levels in each hydrogen atom. Since the number of hydrogen atoms in the tube is very large, the subsequent dropping of electrons to lower-energy levels and the ground state produces all possible transitions. Some transitions occur more frequently than do others.
This produces photons of many different wavelengths the discrete lines we observe in the hydrogen spectrum in the visible and other regions of the electromagnetic spectrum. The Lyman series lines occur in the ultraviolet region, the Balmer are in the visible region, and the Paschen and Brackett are in the infrared.
The wavelength of the photons emitted by the hydrogen atom may also be calculated using the Rydberg equation shown below.
Draw in the observed lines on the above scale and label the colors. Check observed wavelengths against those shown on the spectrum chart in the lab. We use cookies to provide you with a great user experience. By using our site, you accept our use of cookies. Macroeconomics Video Lessons. Accounting Video Lessons. Join Clutch Prep Get a better grade with hundreds of hours of expert tutoring videos for your textbook Continue Continue OR Password must contain at least one uppercase letter, a number and a specific symbol.
Bohr Model Video Lessons. Problem : Which electronic transition in the hydrogen atom results in the emission of light of the shortest wavelength? Problem Details Which electronic transition in the hydrogen atom results in the emission of light of the shortest wavelength? Learn this topic by watching Bohr Model Concept Videos. See all problems in Bohr Model. Frequently Asked Questions What scientific concept do you need to know in order to solve this problem? In , a Danish physicist, Niels Bohr —; Nobel Prize in Physics, , proposed a theoretical model for the hydrogen atom that explained its emission spectrum.
Using classical physics, Niels Bohr showed that the energy of an electron in a particular orbit is given by. In that level, the electron is unbound from the nucleus and the atom has been separated into a negatively charged the electron and a positively charged the nucleus ion.
In this state the radius of the orbit is also infinite. The atom has been ionized. In his final years, he devoted himself to the peaceful application of atomic physics and to resolving political problems arising from the development of atomic weapons.
As n decreases, the energy holding the electron and the nucleus together becomes increasingly negative, the radius of the orbit shrinks and more energy is needed to ionize the atom. Because a hydrogen atom with its one electron in this orbit has the lowest possible energy, this is the ground state the most stable arrangement of electrons for an element or a compound , the most stable arrangement for a hydrogen atom.
Any arrangement of electrons that is higher in energy than the ground state. Except for the negative sign, this is the same equation that Rydberg obtained experimentally. Because a sample of hydrogen contains a large number of atoms, the intensity of the various lines in a line spectrum depends on the number of atoms in each excited state. In contemporary applications, electron transitions are used in timekeeping that needs to be exact.
Telecommunications systems, such as cell phones, depend on timing signals that are accurate to within a millionth of a second per day, as are the devices that control the US power grid. Global positioning system GPS signals must be accurate to within a billionth of a second per day, which is equivalent to gaining or losing no more than one second in 1,, years.
Quantifying time requires finding an event with an interval that repeats on a regular basis. To achieve the accuracy required for modern purposes, physicists have turned to the atom. The current standard used to calibrate clocks is the cesium atom. Supercooled cesium atoms are placed in a vacuum chamber and bombarded with microwaves whose frequencies are carefully controlled.
When the frequency is exactly right, the atoms absorb enough energy to undergo an electronic transition to a higher-energy state. Decay to a lower-energy state emits radiation. In , the second was defined as the duration of 9,,, oscillations of the resonant frequency of a cesium atom, called the cesium clock.
Research is currently under way to develop the next generation of atomic clocks that promise to be even more accurate. Such devices would allow scientists to monitor vanishingly faint electromagnetic signals produced by nerve pathways in the brain and geologists to measure variations in gravitational fields, which cause fluctuations in time, that would aid in the discovery of oil or minerals.
Calculate the wavelength of the lowest-energy line in the Lyman series to three significant figures. In what region of the electromagnetic spectrum does it occur?
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